Raintree:
I will keep this line in mind next time someone has some great unreasonable request for me, but please also remember that when someone has done you favours in the past, this line comes off as ungrateful.

I went over and fed my friend's cats when they were away; drove her to the auto insurance place when her car was totalled even though I didn't particularly feel like it and had to cancel other plans; lent her my camping gear when she didn't have any; found her a job when she lost hers, etc. etc.

Then it came time for me to go away and I needed someone to feed MY cat. She lived three blocks away. I got, "Sorry, that won't be possible."

I resented that. Maybe it really wasn't possible, but I had the feeling she just didn't feel like it. If she had offered some kind of explanation that sounded reasonable, I would have felt less like I'd been used all this time.

wellisawstar:
I would have felt the same way too.

Dindrane:
I've always been under the impression that this particular line really only works well with acquaintances or friends who routinely take advantage of you. I would always think that a good friend, especially one who has done things for me in the past (without complaining or guilt tripping), deserves an explanation. A good friend won't argue with a flat out, "I'm really sorry, I wish I could help, but I just can't this time."

So I agree, Raintree. It would have been nicer if your friend had explained why she can't feed your cat. Especially since it's seems like the kind of thing that can't take more than a few minutes a day.

Emmy:
I agree that this line is a good response for somebody who asks a lot of favors or unreasonable favors, not so much when it comes time to return a favor. In Raintree's case, it sounded like her 'friend' was willing to ask many favors, but unwilling to return them. I would also be resentful in this situation unless my friend had a good reason why she didn't help me out. If I was the OP, my answer to her next favor request would be "I'm afraid that won't be possible".

Lexophile:
This line also works really well when you have a different role at work than you had, say TWO YEARS AGO and people still don't get that.